An LVN is a Licensed Vocational Nurse (LPN--licensed practical nurse in many states). They are basically the licensed nurses who do much of the actual hands on nursing care of patients in the hospitals. In nursing homes they are often the charge nurses.
An RN is a Registered Nurse, also licensed with each state. RN's are taught a much more skilled level of supervising and managing a patient's care, although in some hospitals they are giving all the hands on nursing care. Often, in acute hospitals they may take a few patients to care for themselves, but they are primarily responsible to oversee that doctor's orders are being carried out and manage/supervise both the patient's care and the other employees working with them. An RN can do everything that LVNs and nursing aides do. When I was in nursing school 32 years ago we were constantly told that the RNs are the supervisors and managers.
There are a number of things that LVNs cannot do. An LVN cannot do IV's unless they take a special course and become certified to do it (depending on their state requirements), and even then there are certain medications and IV fluids that they cannot give patients. Both RNs and LVNs can give medications, but only RNs can give IV push medications. In most states only RNs can take doctor's orders and write them in patient's charts in the acute hospitals. However, in nursing homes, LVNs usually are allowed to do this.
Over the years there has been discussion from time to time to eliminate the level of LVN/LPN. This is because as technology has advanced and the RN shortage seems to wax and wane, a lot of nursing leaders felt that LVN/LPNs were being allowed by states to do more and more of the RNs work, so why not just grandfather them up to RNs and eliminate the LVN/LPN designation. This was discussed when I was in nursing school 32 years ago and still goes on. Right now, because there is supposedly a shortage or RNs (depending on where you live in the country), this discussion may or may not be going on. 30 years ago LVNs did not give medications or do anything at all with IVs. Just to give you an idea of how things have changed, 30 years ago my mother was an LVN in the hospital where I worked as an RN. My mother took care of patients, changed their dressings, gave baths, walked the patients, etc. I was a team leader and although I did some nursing care, I was primarily involved in making rounds with doctors, making sure the doctor's orders were carried out, passing medications and taking care of all the IV needs of patients.